1. The problem statement, all variables and given/known data Find the total magnetic force on the semi-circular part of the conductor. There is a current I running counterclockwise through the semi-circle. The magnetic field B is out of the page. 2. Relevant equations F = Il x B l = Rθ dl = Rdθ 3. The attempt at a solution I assumed that the force is anywhere perpendicular to the conductor, so I disregarded the cross product and used F = IlB, where l is the length of the conductor. So, dF = IBdl = IBRdθ I then went ahead and integrated the dθ (upper limit: pi, lower limit: zero) and retrieved an answer of pi*IBR for the total force. The book states that the answer is 2*IBR, and they get this answer by breaking up the dF force into an x-component IBRcosθdθ and a y-component IBRsinθdθ and then integrating these two components from lower limit of zero to upper limit of pi. Why is it necessary to break the dF into x and y components and integrating these components, rather than just integrating the total force dF? I've thought about it for a while but can't figure out why my method was incorrect. Thanks.